Identification of efficient COVID-19 diagnostic test through artificial neural networks approach − substantiated by modeling and simulation

1.1 Literature review

Though a considerable progress has been made since the first COVID-19 case reported in Wuhan, China, it still needs our efforts to contain its spread to resume the activities back to normal as early as possible and ultimately lessening the burden on the global economy. Considering the minimal potential to test and handle a massive influx of patients even after a year of the pandemic, we need to devise solutions to increase the efficiency without altering the specificity of testing that will ultimately reduce the burden on pharmaceutical and manufacturing companies and the local healthcare sectors as well [4]. Efforts were being made in this regard at the federal and state levels and were disbursed at a local level to provide better living and healthcare facilities to communities. Strategies were being designed to eliminate the need for extended stay-at-home instructions when enforcing risk-based lockdown, testing, touch-tracking, and surveillance procedures as the economic woes of the COVID-19 pandemic intensify [5]. Given the scarce resources and the critical fiscal, public health, and organizational complexities of the existing 14-days quarantine recommendation, it is important to understand whether it is possible to introduce more efficient yet similarly effective testing techniques [5,6]. Therefore, it is the need of the time to improve the testing capacity and timely tackle and control COVID-19 cases. This would not only help in resuming the work, reducing the losses by the corporate sector but also can be taken as an opportunity to meet the needs of the shackled healthcare system in this pandemic.

Amid this healthcare challenge, out of many hard-hit sectors, the corporate sector was one of the main affectees that has faced a considerable setback due to jamming of all sorts of activities in every domain. COVID-19 has shaken not only the healthcare sector but has caused a considerable damage to businesses around the globe as well. Companies that offer information services continued to survive while manufacturing companies had to either close their workplaces or allow workers conditionally with stringent instructions of maintaining social distancing, avoiding congregations, and proper use of PPE. Under the domain of manufacturing enterprises, only those who were producing basic goods were allowed to operate [7]. And, the effect of these restrictions on all sorts of activities when evaluated was in the form of huge financial losses for small businesses due to disruption of the supply chain, reduced profits, and product demand. Due to these reasons, some enterprises could not survive the lockdown and were permanently closed while others are on the verge of collapsing if it continues for 2 or more months [8]. The main reason was found to be a lack of preparedness toward handling a pandemic by over 83% of these micro, small, and medium enterprises. The ultimate consequences can be observed in terms of economic disparity and increased joblessness in the past few months. Therefore, in some countries, a support package was launched to sustain these businesses [9]. But as the pandemic has struck again vivaciously, providing a support package is not sufficient and requires some preventive and control measures as well. Testing being the cornerstone of identifying COVID-19 positive cases is a need of all the enterprises and of every sector that had to shut down its activities under government instructions. To overcome the adversities of pandemic and to resume the activities back to normal by all the surviving enterprises, it is important to test individuals for COVID-19 before officially restoring the operational activities. But a single PCR-based test costs around $100, so it is economically not feasible for businesses to conduct tests of all the employees after facing an economic blow due to the current pandemic [10].

At present, COVID-19 tests approved by U.S Food and Drug Administration are classified as either diagnostic tests or antibody test both of which detects COVID-19 infection differently. Diagnostic tests can be done by detecting viral genetic material via Reverse Transcriptase Polymerase Chain Reaction (RT-PCR) or it can be performed by detecting viral antigens in the test samples. Antibody test, on the other hand, detects the presence of antibodies against the viral antigen. The diagnostic test is usually performed on fresh swabs taken from individuals to detect viral load while an antibody test is performed on individuals who are already exposed to COVID-19 and have antibodies in the blood against the virus. An antibody test cannot be used to diagnose COVID-19 because antibodies sometimes take a week or more to be synthesized against the virus after initial infection and their levels can be detected even after recovering from COVID-19. Therefore, it cannot tell exactly if the body is still carrying the viral load. The only reliable way to detect the viral load of COVID-19 is through diagnostic tests that can indicate an active infection in the individual [11]. But each of these methods has its own drawbacks as well, depending on the context of testing done. Apart from these, radiology has also found its role in identifying COVID-19 cases by using chest X-rays and CT scans. These radiographs indicate the abnormalities in the lungs but cannot be taken as a way to detect COVID-19 [12]. Out of all these mentioned techniques for COVID-19 testing, the most reliable is RT-PCR-based testing (Table 1). Thus, after identifying the most effective type of diagnostic test, it is important to improve the capacity of already existing techniques so that a maximum number of individuals could be tested for COVID-19 that would ultimately help in identifying disease hotspots and tracing points of contact. As carrying out screening tests on a large scale is not possible with limited resources, Artificial Intelligence and Machine Learning are introduced into the healthcare sector to improve the working capacity with limited available resources.

By using data from diagnostic tests and X-rays or CT scans, AI and ML tools were utilized to improve the detection and tracking of COVID-19 [13,14,15,16,17]. However, these models have limitations in real-world implications despite being them up-to-the mark. Also, most of these studies include a pre-detection technique involved, whether it’s an X-ray or CT scan. Mohammed et al. brought a novel strategy of predicting the cases through true positive and negative Mathew’s correlation sensitive analysis merged with entropy and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) but again the input data has to have previous reliability on other detection methods, which involves regressive and expensive techniques. Moreover, this study is relied on laboratory- and hospital-based data and feature selection [18]. In previous studies, chest CT scans were integrated with clinical symptoms by using AI that helped in improving the detection of COVID-19 even in cases in which a normal CT scan was obtained [19]. AI also helped in differentiating COVID-19 from community-acquired infections like pneumonia [20]. It also contributed to coupling of self-testing with disease tracking which would help in containing the spread of disease [21]. Many COVID-19 hotspots were detected by using AI and it was also used to predict the future hotspots [22]. All these studies demonstrated the use of AI and ML in the healthcare sector, particularly in the case of a pandemic. It should be noted here that in all these AI- and ML-based studies, the area of focus remained improving radiological findings by utilizing chest X-rays and CT scan images of normal and COVID-positive individuals. These tests are not approved as COVID-19 diagnostic tests, but in case of any emergency situation, they can be used to identify the extent of infection in individuals that when combined with clinical symptoms may indicate COVID-19 infection. Therefore, our study utilizes AI for improving the capacity for RT-PCR that is the gold standard for COVID-19 diagnosis. These findings will provide a cost-effective testing solution for the healthcare sector and manufacturing enterprises as well.

This study analyses the effectiveness of pooled testing of COVID-19 through ANN approach and Machine Learning by using binary search. For validating the hypothesis, ANN and Machine Learning were used as they have shown high performance in obtaining and interpreting huge volumes of data [23]. It works on similar principles as of the human brain in which the input signal after processing gives an output. In the same way, data fed in ANN are interpreted in different layers, and the results are displayed through the output layer. In the simplest model, three layers exist that are input layer, hidden layer, and output layer. But the intermediate hidden layers may increase in number depending on the amount of information and its complexity [24]. ANN though works on similar principles of human brains, but its processing and results are more profound than a human brain. Its capacity to solve problems that are almost impossible for humans make it an efficient tool used in Artificial Intelligence (AI) and is, therefore, used in this study as well to analyze and model the huge volumes of data fed through the input layer [23,25]. Machine Learning tools were then applied to the data generated through ANN, and by using the binary search tool, the data was sorted. The binary search tool has advantages over linear search as it can sort large volumes of data effectively in a short time and, therefore, is more suitable for sorting population-based data.

In this study, we have collected bibliometric data that are analyzed through the ANN approach and by Machine Learning have developed algorithms. These algorithms were used in evaluating the efficiency of sample pooling first with eight samples that were later extended to 16 samples. On this basis, in this study, it is proposed that pooling of samples will not only increase the testing capacity but also work without altering the specificity of the testing procedure that will stay the same 96% even with a pool of 16 samples. This will help in reducing the cost and will prove highly economical in population-based studies where the prevalence rate of diseases is usually low. It will be helpful not only in detecting COVID-19 cases but also in testing both symptomatic and asymptomatic carriers and tracing the points of contact in limited resources [26]. Due to these reasons, it will stand in a more economical position than the current strategy of individual testing that no doubt if has merits, also has demerits of an economic burden on the healthcare sector and an increased consumer demand for manufacturing companies. Therefore, introducing Artificial Intelligence in the healthcare sector not only will provide cost-effective solutions to enterprises but will also provide evidence for further research in the healthcare domain [27]. The ease in scientific data collection by accessing it through devices like antennas and wireless devices has transformed the biotechnology sector by giving smart solutions for healthy lifestyle and wellbeing of people [28,29]. Thus, this study conducted by applying principles of AI will provide grounds to decision-makers to enhance the testing capacity within limited resources and to introduce new strategies to control and confine the pandemic.

2.1 The dataset used

A dataset containing citation information must be collected before starting any bibliometric analysis. Therefore, data were retrieved from databases including PubMed, Scopus, and Web of Science by using keywords related to COVID-19 and was further evaluated.

2.2 Proposed methodology

The available information from different Internet sources was obtained for bibliometric analysis. It was further evaluated by using the ANN approach. The output information from ANN was obtained in the form of a map that was constructed by VOSviewer software. The output was further analyzed via MATLAB where probabilistic algorithms were applied to find out the probability of effectiveness of our proposed solution. A collective summary of all the components of the Artificial Intelligence and Machine Learning model adopted for this research is schematically depicted in Figure 1.

Figure 1

Workflow of study.

3.1 Experimental setup

3.1.3 Mathematical algorithms

Information obtained from the ANN model was further analyzed. It was subjected to MATLAB that helped in statistically validating the probability of our proposed solution. Therefore, we started this study by taking samples in power of two, so that there can be a total of l = log₂ N levels. The model generated was elaborated by using a group of eight individuals. Figure 2 represents all eight samples arranged in four levels. These samples from S1 to S8 belong to eight different individuals and represent the lowest level, level 4. These samples are then paired to give a higher level, level 3, in which four pairs will be formed from eight samples. Pairs from level 3 will again cluster to give level 2 with four samples in each cluster that is ultimately pooled up to give level 1 with all eight available samples. From level L₁ to L _l-1, each sample is formed by adding two child samples of succeeding level such that

S ( i ) = S ( i – 2 L ) + S ( i + 1 – 2 L ) ,

where S ( i −   2 L )   and S ( i + 1 − 2 L ) become child samples of S(i)

Figure 2

Sample pooling of eight samples in four levels.

In this approach instead of testing all the samples in a linear fashion, we started from the highest level 1 with all samples, i.e., S(2 ^L − 1) pooled, and if sample S(i) comes out positive, both child samples of S(i) will be tested. By this approach, a possible number of tests to diagnose eight people are t such that t ∈ {1, 7, 9, 11, 13, 15}. All the possible values of t are elaborated in the given figures.

As depicted in Figure 3, if all the samples pooled in S(15) are COVID-19 negative, they will be tested by only a single test performed on this pool of samples. This will be the most effective way in which a minimum number of tests will be performed.

Figure 3

One test to be performed for testing eight individuals.

Figure 4 shows the number of tests to be performed if either both or one sample of a pair is positive for COVID-19. In such instances, it can be evaluated by performing seven tests starting from level 1 to level 4.

Figure 4

Seven tests to be performed for testing eight individuals.

Figure 5 represents a scenario in which nine tests will be performed to test eight individuals when either both samples or one sample from both pairs of the same cluster are detected positive.

Figure 5

Nine tests to be performed for testing eight individuals.

Figure 6 represents the situation when either both samples or samples from a single pair of both clusters are positive and can be tested by performing a total of 11 tests.

Figure 6

Eleven tests to be performed for testing eight individuals.

Figure 7 reflects the number of tests to be performed when one or both samples of three pairs from both the clusters are COVID-19 positive will be 13. A total number of tests performed will increase to 15 tests in situations when either both or a single sample from each pair of both clusters is positive. This is shown in Figure 8 and will give the maximum number of tests that will be performed from pooling samples from eight individuals.

Figure 7

Thirteen tests to be performed to test eight individuals.

Figure 8

Fifteen tests to be performed to test eight individuals.

All this information on sample pooling suggests that sample pooling for eight individuals will be valuable only when the probability of occurrence of positive cases is low. Therefore, it will be beneficial in epidemics or pandemics when the prevalence rate is low, and there are more chances of getting a negative result than a positive result. If p is the probability of a positive outcome of a test, the probability of the possible number of tests then becomes

P [ t ] = ( 1 − p ) 8 ; t = 1 4 ( 2 p – p 2 ) ( 1 – p ) 6 ; t = 7 2 ( 2 p – p 2 ) 2 ( 1 – p ) 4 ; t = 9 4 ( 2 p – p 2 ) 2 ( 1 – p ) 4 ; t = 11 4 ( 2 p – p 2 ) 3 ( 1 – p ) 2 ; t = 13 ( 2 p – p 2 ) 4 ; t = 15 .

The average number of tests E[t ₈] that this strategy takes as a function of probability p for a pool of eight people is given as follows:

E [ t 8 ] = − 2 p 8 + 16 p 7 − 56 p 6 + 112 p 5 − 144 p 4 + 128 p 3 − 88 p 2 + 48 p + 1 .

As discussed earlier, the number of samples can be taken in the power of two. Therefore, if the number of samples is increased from 8 to 16 samples, then a total of five levels will be made to evaluate the number of tests performed. Therefore, the number of tests performed for all negative cases will be one, and the maximum possible tests performed when either one or two samples of all the pairs are positive will be 31.

Hence, the maximum possible number of tests for 16 samples pooling (t ₁₆) is given by

∈ { 1 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , 31 } .

The probability for the possible number of tests performed by pooling samples of 16 individuals is discussed by the given algorithm.

P [ t 16 ] = ( 1 − p ) 16 ; t = 1 8 ( 2 p  –  p 2 ) ( p − 1 ) 14 ;  t = 9 4 ( 2 p – p 2 ) 2 ( p − 1 ) 12 ; t = 11 8 ( 2 p – p 2 ) 2 ( p − 1 ) 12 ; t = 13 8 ( 2 p – p 2 ) 3 ( p − 1 ) 10 + 4 ( 2 p – p 2 ) 2 ( p − 1 ) 12 ; t = 15 2 ( 2 p – p 2 ) 4 ( p − 1 ) 8 + 4 ( 2 p – p 2 ) ( 2 p – p 2 ) ( p − 1 ) 10 ; t = 17 4 ( 2 p – p 2 ) 4 ( 2 p – p 2 ) 8 + 8 ( 2 p – p 2 ) 2 ( 2 p – p 2 ) ( p − 1 ) 10 ; t = 19 16 ( 2 p – p 2 ) 4 ( p – 1 ) 8 + 8 ( 2 p – p 2 ) 3 4 ( 2 p – p 2 ) ( p − 1 ) 8 ; t = 21 16 ( 2 p – p 2 ) 5 ( p – 1 ) 6 + 16 ( 2 p – p 2 ) 4 ( p − 1 ) 8 + 2 ( 2 p – p 2 ) 4 4 ( 2 p – p 2 ) ( p − 1 ) 6 ; t = 23 4 ( 2 p – p 2 ) 6 ( p – 1 ) 4 + 32 ( 2 p – p 2 ) 5 ( p – 1 ) 6 ; t = 25 24 ( 2 p – p 2 ) 6 ( p − 1 ) 4 ; t = 27 8 ( 2 p – p 2 ) 7 ( p − 1 ) 2 ; t = 29 ( 2 p – p 2 ) 8 ; t = 31 .

Mean for 16 person’s sample becomes

E [ t 16 ] = ( p − 1 ) 16 + 232 ( 2 p – p 2 ) 7 ( p − 1 ) 2 + 748 ( 2 p – p 2 ) 6 ( p − 1 ) 4 + 1 , 168 ( 2 p – p 2 ) 5 ( p − 1 ) 6 + 814 ( 2 p – p 2 ) 4 ( p − 1 ) 8 + 120 ( 2 p – p 2 ) 3 ( p − 1 ) 10 + 148 ( 2 p – p 2 ) 2 ( p − 1 ) 12 + 15 ( 2 p – p 2 ) 2 ( p − 1 ) 12 + 31 ( 2 p – p 2 ) 8 + 72 ( 2 p – p 2 ) ( p − 1 ) 14 + 46 ( 2 p – p 2 ) 16 ( 2 p – p 2 ) ( p – 1 ) 6 + 168 ( 2 p – p 2 ) 3 4 ( 2 p – p 2 ) ( p – 1 ) 8 + 220 ( 2 p – p 2 ) 2 4 ( 2 p – p 2 ) ( p – 1 ) 10 . .

By using these above-mentioned algorithms, the probability of effectiveness of our proposed solution was evaluated for sample pools of eight individuals and 16 individuals.

4.1 Bibliometric analysis and ANN model

Bibliometric data fed into the ANN model were obtained for analysis through the output layer in the form of a map by using VOSviewer software. The map shows the most searched topics with reference to COVID-19 and is given in Figure 9.

Figure 9

Keywords found in the literature related to COVID-19 testing.

The nodes on this map depict that the most repetitive keywords found in the literature retrieved through different search engines were COVID-19, machine learning, deep learning, ANN, pandemic, chest X-ray, computed tomography, etc. This shows the data collected for this research revolved around the COVID-19 testing and involves the application of AI and ML in controlling the pandemic. It can be seen in Figure 9 that CT scans and chest X-rays were already being under research for their role in identifying COVID-19. Therefore, after careful analysis, it was decided to improve the working capacity of a gold standard of COVID-19 testing that is RT-PCR. Though area of research of many artificial intelligence-based studies revolved around chest X-rays and CT scans, but due to their limitations and inefficiency in correctly detecting COVID-19, we evaluated a different testing strategy focusing on pooling swabs for COVID-19 diagnosis.

4.2 Comparison and analysis of COVID-19 linear and pooled testing

Probabilistic results were obtained by applying the above-mentioned algorithms. The results obtained are discussed here.

Figure 10a demonstrates the average tests that need to be performed for both linear and pooled testing, when the probability of getting a positive result increases. For linear testing, it can be seen that number of tests is neither increasing nor decreasing for both eight individuals testing and 16 individuals testing. However, a rising curve is obtained for pooled testing that increases sharply in the beginning and then after a certain point attains a steady state. This shows that when the probability of getting a positive result is as low as 20%, the average number of tests to be performed on a pooled sample is lower than the number of tests performed for linear testing. After 20%, it can be seen that number of tests for pooled testing increases than for linear testing, making it the least viable solution in cases where the probability of getting a positive sample is higher.

Figure 10

(a) Average tests are required for linear and pooled testing. (b) An average number of people tested with one test. (c) The average number of tests required per person for linear and pooled testing.

Figure 10b represents the number of people that can be tested by using only one test when the probability of getting a positive result increases. It can be seen that for linear testing a straight line is obtained showing that only one person will be tested with one test. However, for pooled testing, a sudden decline in the curve can be seen that shows that when the probability of getting a positive is as low as 0%, one test is sufficient to test a pooled sample of either 8 individuals or 16 individuals. However, as the probability starts increasing, the number of tests that should be performed to test samples would also increase. The probability at the point of intersection of all three lines indicates that sample pooling would be an effective and time-saving technique before that point of 19% probability. But, if probability will increase beyond that point, sample pooling will lose all of its effectiveness, and therefore, it will no longer be a recommended testing approach.

Figure 10c compares a number of tests required per person for linear testing with pooled testing. A straight line for linear testing represents that one test will be required to test one person irrespective of the probability of getting a positive or negative result. However, for pooled samples, a rising curve is obtained that rises sharply at the beginning when the probability of getting a positive result is low. These rising curves show that the average number of tests per person performed on pooled samples will be low when probability will be low and as soon as the probability increases to 19%, after that, it is no longer significant and the average test per person will start to increase in that case. The point of intersection of these lines demonstrates that sample pooling will be effective only when the probability of getting a positive is low.

All these results suggest that sample pooling holds potential benefits over linear testing, but only in instances when the probability of getting a positive result is low. This suggests that for diseases having a low prevalence rate in different communities, sample pooling would be an effective technique for detecting the disease and taking timely actions. As the prevalence of COVID-19 is low in many countries, this study provides a statistically proven solution, demonstrating the effectiveness of sample pooling in maximizing the number of individuals to be tested.

4.3 Case study based on our proposed algorithm

Adopting this approach, a case study was conducted in the Punjab region when positive detection probability was reported to be 6%. In this case study, several tests were conducted with the group pooling of 16 samples in each test. The abovementioned algorithms were applied, and the probability against each case was evaluated. The graph in Figure 11 shows percentages of tests to be performed for each sample pool.

Figure 11

Population-based study with seven sample pools of 16 individuals each.

All these results obtained from applying algorithms to find out the efficiency of our proposed solution suggest that for population-based studies for diseases that have a low prevalence rate, sample pooling is an effective means of increasing the capacity of testing with minimum available resources. As COVID-19 prevalence is low in many communities, our study will provide scientific grounds to incorporate better and improved solutions in the healthcare sector.

4.4 Application of the algorithm on other countries

Evidently, the probability of the number of tests increases with the Covid positive occurrence for each state mentioned (Figure 12). There is a 98% probability for New Zealand and Australia to have detected a Covid case with the sample pooling suggested above. With the increase in Covid Positive ratio, there is a decline in the percentage of positive test detection. The minimum number of tests performed on a high positive ratio for 16 people pool is 10 with the probability of approx. 40% for USA. For Germany, there need to be 10 repetitions of the test to reach a 30% probability. The recent data available from the source mentioned in Figure 12 can be imported into the supporting file to extrapolate results.

Figure 12

Test predictions for five major countries hit as of 21/04/2021(The COVID +ve ratio is adapted from https://ourworldindata.org/coronavirus-testing).